Heat the oil in a large saucepan. Add the parsnips, celery root, carrots, potato, leek, garlic, thyme, 1/2 teaspoon of salt and 1/2 cup of water. Cook over moderately high heat, stirring, until the liquid has evaporated and the vegetables start to brown, about 10 minutes. Add the stock, cover the pan and reduce the heat to moderately low. Cook until the vegetables are very tender, about 30 minutes.